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Epitaxial and atomically smooth ultra-thin SrCuO2 films are grown on SrTiO3 substrates using pulsed laser deposition. The structural and chemical aspects of these single-layer films of various thickness are characterized using in situ X-ray photoelectron diffraction (XPD) and photoelectron spectroscopy. By comparing XPD scans to multiple-scattering electron diffraction simulations, we demonstrate a structural transformation from bulk-planar to chain-type SrCuO2 as the film thickness is reduced from 9 to 3 unit-cells. This observation is in agreement with the recent theoretical prediction [Z. Zhong, G. Koster, and P. J. Kelly, Phys. Rev. B 85, 121411(R) (2012)] and opens new pathways for structural tuning in ultra-thin films of polar cuprates.